(121212......300 Times)/99 -  What is the remainder?

Solution:

If I want to find the remainder when a number is divided by 99, then I start from the unit's digit of the number, take two digits at a time and then move towards the leftmost digit finding the sum of all those two digit numbers obtained and then find the remainder when that sum is divided by 99.

Example:

What is the remainder when the number 1234567 is divided by 99?

In number theory, the totient ( also called phi) Φ (n) of a positive integer n is defined as the number of positive integers less than or equal to n that are co prime to n.

For example, Φ(9) = 6 since the six numbers 1, 2, 4, 5, 7 and 8 are co prime to 9.
A few first values: Φ (1)=1, Φ (2)=1, Φ (3)=2, Φ (4)=2, Φ (5)=4, Φ (6)=2, Φ (7)=6, Φ (8)=4, Φ (9)=6, Φ (10)=4, Φ (11)=10, Φ (12)=4, Φ (13)=12, etc., do not appear to follow any law. But there is a formula discovered by Euler to which helps in calculating these numbers.